The Gunners are expected to strengthen their squad this month, having already offloaded Moroccan misfit Marouane Chamakh on a six-month loan deal to West Ham.
Arsenal manager Arsene Wenger is said to be keen on Villa, who was a substitute for Barcelona's 4-0 win over Espanyol at the weekend.
Rosell, however, maintains the 31-year-old, signed in a £31 million deal from Valencia in 2010, is going nowhere.
Speaking to Catalan radio station RAC1, Rosell said: "I completely rule out the transfer of Villa during the winter market.
"He is ours and we need him, there is a lot of the season left."
Arsenal are also reported to be in for Atletico Madrid frontman Adrian Lopez, while Wenger is claimed to be looking at further midfield options, with Anderlecht's Argentina international Lucas Biglia said to be on his radar.
Sao Paulo, meanwhile, are confident they can turn Denilson's loan move into a permanent transfer.
Arsenal now head into a crucial run of fixtures which could define their season.
Following a dramatic 2-2 draw at Swansea in the FA Cup, the Gunners face a replay next week just a few days after Barclays Premier League champions Manchester City come to Emirates Stadium.
Arsenal then travel to Chelsea on January 20, before tackling West Ham in their rearranged Boxing Day fixture, which is followed by a possible FA Cup fourth-round tie at Brighton ahead of the visit of Liverpool.
Defender Per Mertesacker feels the Gunners can meet their busy schedule head on.
He said: "We are in a good way but we have to keep our focus on these games [against Manchester City and Chelsea] and the knockout stages of the Champions League. We have to win those games now," the German centre-back said.
"We are always looking to win something and we can achieve something with this group. We have a lively group so our thoughts are now on the next match, that is the most important thing for us, not what's going to happen in May.
"We have a few targets in our team that are possible this year. We won't talk about it, we'll just see what happens in the next few important weeks on the pitch."